Monday, January 11, 2016

Thales UK has been investigating the use of Homomorphic Encryption
(HE) in satellite scenarios. In particular, our assessment has focused on the
data processing of imaging products; one of the many types of signal processing
applications which could have been chosen.

It is relatively simple to find signal processing
satellite applications where HE could, in theory at least, provide real benefit. In particular, to
provide end-to-end security of data from the sensor on the satellite to the end
user, while allowing the potentially complex and specialised signal processing
to be performed on shared (and less trusted from the end user’s point of view)
infrastructure. The real challenge has been to find such applications that are
potentially practical in the near term, using Somewhat Homomorphic Encryption
(SHE).

Consider the Sentinel 2 Multi Spectral Imager
which is a representative example of an earth observation satellite (in this
case designed for environmental monitoring). In order to be suitable for the
application of HE to provide sensor to end user security, all the signal
processing algorithms would have to be amenable to HE. It turns out that many
of them potentially are, in particular the deconvolution algorithms that use
Fourier Transforms. However, other parts of the processing are more difficult
to deal with in HE. For example, processing to deal with imperfections such as:

saturated pixels

no data pixels and
partially corrected pixels (crosstalk correction)

defective pixels

These are very simple algorithms, but involve a lot of
conditional operators (<, >, etc. to test pixel values) that wouldbe expensive
when implemented on HE encrypted data.

A much more promising candidate is Synthetic Aperture Radar
(SAR) (e.g. Envisat).
SAR is used to provide high precision, and often 3D, imaging for applications
such as sea ice and glacier monitoring, vegetation coverage analysis, disaster
monitoring and traffic surveillance. Being a radio-based technique, it is not
affected by weather or the lack of daylight. The raw data collected by the
satellite consists of a series of radar echoes, and these must be processed to
form an image. On examining the details of this processing, it can be seen that
the core functionality consists of a series of:

Fourier Transforms (and their
inverses)

Hadamard products of matrices

These can be implemented, in theory at least, with a low
multiplicative depth, and without the need for conditional operators. This is
therefore a good candidate application for SHE, but much work needs to be done
to demonstrate its practicality.